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Simplifying x5 + -1x + -4x3 = 0 Reorder the terms: -1x + -4x3 + x5 = 0 Solving -1x + -4x3 + x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-1 + -4x2 + x4) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-1 + -4x2 + x4)' equal to zero and attempt to solve: Simplifying -1 + -4x2 + x4 = 0 Solving -1 + -4x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -4x2 + 1 + x4 = 0 + 1 Reorder the terms: -1 + 1 + -4x2 + x4 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4x2 + x4 = 0 + 1 -4x2 + x4 = 0 + 1 Combine like terms: 0 + 1 = 1 -4x2 + x4 = 1 The x term is -4x2. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x2 + 4 + x4 = 1 + 4 Reorder the terms: 4 + -4x2 + x4 = 1 + 4 Combine like terms: 1 + 4 = 5 4 + -4x2 + x4 = 5 Factor a perfect square on the left side: (x2 + -2)(x2 + -2) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x2 + -2) equal to 2.236067978 and -2.236067978.Subproblem 1
x2 + -2 = 2.236067978 Simplifying x2 + -2 = 2.236067978 Reorder the terms: -2 + x2 = 2.236067978 Solving -2 + x2 = 2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x2 = 2.236067978 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = 2.236067978 + 2 x2 = 2.236067978 + 2 Combine like terms: 2.236067978 + 2 = 4.236067978 x2 = 4.236067978 Simplifying x2 = 4.236067978 Take the square root of each side: x = {-2.058171027, 2.058171027}Subproblem 2
x2 + -2 = -2.236067978 Simplifying x2 + -2 = -2.236067978 Reorder the terms: -2 + x2 = -2.236067978 Solving -2 + x2 = -2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x2 = -2.236067978 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = -2.236067978 + 2 x2 = -2.236067978 + 2 Combine like terms: -2.236067978 + 2 = -0.236067978 x2 = -0.236067978 Simplifying x2 = -0.236067978 Reorder the terms: 0.236067978 + x2 = -0.236067978 + 0.236067978 Combine like terms: -0.236067978 + 0.236067978 = 0.000000000 0.236067978 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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